solve using elmination method
2x-6y=2
-8x+6y=26
To solve the system of equations using the elimination method, follow these steps:
Step 1: Align the equations vertically.
2x - 6y = 2
-8x + 6y = 26
Step 2: Choose one variable to eliminate by multiplying one or both equations by a suitable number.
In this case, we can eliminate the y variable by multiplying the first equation by 1 and the second equation by -1. This will result in adding the equations to eliminate the y terms.
(1) * (2x - 6y) = (1) * (2)
(-1) * (-8x + 6y) = (-1) * (26)
Which becomes:
2x - 6y = 2
8x - 6y = -26
Step 3: Add the equations together, canceling out the variable that we chose to eliminate in Step 2.
(2x - 6y) + (8x - 6y) = 2 + (-26)
2x + 8x - 6y - 6y = 2 - 26
10x - 12y = -24
Step 4: Simplify the equation obtained in Step 3.
10x - 12y = -24
Step 5: Solve the simplified equation for one variable.
Let's solve for x:
10x - 12y = -24
Divide both sides of the equation by 10:
(10x - 12y) / 10 = -24 / 10
x - (12/10)y = -12/10
x - (6/5)y = -6/5
x - (6/5)y = -1.2
Step 6: Substitute the value of the solved variable back into one of the original equations to solve for the other variable.
Substitute x = -1.2 into either of the original equations. Let's use the first equation:
2x - 6y = 2
2(-1.2) - 6y = 2
-2.4 - 6y = 2
-6y = 2 + 2.4
-6y = 4.4
y = 4.4 / -6
y = -0.73
So, the solution to the system of equations is:
x = -1.2
y = -0.73